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Uniqueness of the measure with full dimension on sofic affine-invariant subsets of the 2-torus

Published online by Cambridge University Press:  12 August 2009

ERIC OLIVIER
ERIC OLIVIER*
Affiliation:
Université de Provence, LATP (CNRS-UMR 6632), Marseille, France (email: eric.olivier@univ-provence.fr)
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Abstract

We consider the variational principle for dimension on compact subsets of the 2-torus which are invariant under a non-conformal expanding diagonal endomorphism. Condition (H) ensures that the invariant measures with full dimension are the equilibrium states of some potential function. This result applies to the problem of uniqueness of the measure with full dimension on the sofic affine-invariant sets.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 5 , October 2010 , pp. 1503 - 1528
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Copyright © Cambridge University Press 2009

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